The finite difference method M₃ developed in Ref. [4] by Chawla and Katti for singular two point boundary value problems with p(x) = x^b₀, 0 ≤ b₀ < 1 and boundary conditions y(0) = A, y(1) = B (A, B are constants) has been extended for the singular boundary value problems with general function p(x) = x^b₀ g(x), 0 ≤ b₀ < 1 and the boundary conditions Second order convergence of the method has been established for quite general conditions. Numerical examples for general function p(x) verify the order of convergence of the method.